Pith Number

pith:ATEK4JK2

pith:2011:ATEK4JK2LXUBXQMC2CHE355ZOT

not attested not anchored not stored refs pending

The non-commutative A-polynomial of (-2,3,n) pretzel knots

Christoph Koutschan, Stavros Garoufalidis

arxiv:1101.2844 v4 · 2011-01-14 · math.GT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATEK4JK2LXUBXQMC2CHE355ZOT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:45:43.879481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04c8ae255a5de81bc182d08e4df7b974de80dafe8dca2c4054250c794ca14437

Aliases

arxiv: 1101.2844 · arxiv_version: 1101.2844v4 · doi: 10.48550/arxiv.1101.2844 · pith_short_12: ATEK4JK2LXUB · pith_short_16: ATEK4JK2LXUBXQMC · pith_short_8: ATEK4JK2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ATEK4JK2LXUBXQMC2CHE355ZOT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 04c8ae255a5de81bc182d08e4df7b974de80dafe8dca2c4054250c794ca14437

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5ba4f3274a16cfd722d86ac604bd794dedf91babb87501e5526e3d8fe3a1840",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-01-14T15:43:16Z",
    "title_canon_sha256": "b04bb34a576a0d8768ba911a30b1b3af69a267584917bd15cab45e62d6baf0d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2844",
    "kind": "arxiv",
    "version": 4
  }
}